1. Realized Volatility

To estimate daily volatility of equity returns, we can use the intraday data, in particular, the intraday returns. Since the expected value of the intraday returns is zero, a good estimator of variance is the sum of the squared returns.

We can now compute the realized variance for each day:

# A tibble: 5,607 x 3
   index_date        RV   RVol
   <date>         <dbl>  <dbl>
 1 1996-01-02 0.000180  0.213 
 2 1996-01-03 0.000272  0.262 
 3 1996-01-04 0.0000380 0.0979
 4 1996-01-05 0.0000422 0.103 
 5 1996-01-08 0.0000218 0.0740
 6 1996-01-09 0.0000478 0.110 
 7 1996-01-10 0.0000542 0.117 
 8 1996-01-11 0.0000553 0.118 
 9 1996-01-12 0.0000538 0.116 
10 1996-01-15 0.0000367 0.0962
# ... with 5,597 more rows

Now let’s plot the RVs:

Let’s check the ACF on the RVs:

2. RV Sparse

An RV Sparse estimator consists of calculating the realized variance but with a sample that is less frequent than the 1-minute grid. Instead, it is sampled in an s-minute grid (where \(s \geq 1\)).

Here, we will use different combinations of \(s\) such as s = 5, s = 10, s = 15, and s = 30. In order to plot a signature plot, we will also sample from \(s \in [1, 120]\).

Realized Higher Moment Measures

1. Realized Volatility

2. RV Sparse